Strongly Anisotropic Band Dispersion of an Image State Located above Metallic Nanowires

Abstract

Indium can be grown on Si(111) in a 4 3 1 pattern that contains rows of In atoms spaced 13.3 Å apart that have quasi-one-dimensional electronic structure. This ordered array of metallic wires produces an image-induced surface state series. We have measured the dispersion of the most tightly bound ͑n 1͒ image state band and found it to be unconventional because it falls below the free electron parabola perpendicular to the In atom rows. The most straightforward explanation for this is that the electrons feel the surface corrugation potential produced by the rows of In atoms. We were able to infer the form of the potential from our measurements. [S0031-9007 (99)08625-1] PACS numbers: 73.20.At, 73.20.Dx Indium can be grown on Si(111) in a 4 3 1 pattern [1], that contains long rows of In atoms [2-6] that are either 2 or 3 atoms wide [3] with a center-to-center separation of 13.3 Å. The surface reconstruction is complex and still under active study. Candidate structures conveniently divide into two categories. There are those that place the In atoms on a largely unreconstructed Si(111) surface [3,7,8] and those that require the uppermost Si layer to reconstruct [6]. The electronic structure of the 4 3 1 phase has also been the subject of intense study. Recent photoemission [9], inverse photoemission [10-12], and STM [4] studies have provided compelling evidence that the 4 3 1 phase is both quasi-1D and metallic. It is the latter property that sets the 4 3 1 system apart from other quasi-1D systems like the insulating Si(111)-M͑3 3 1͒ (where M ͕Li, Na, K, and Ag͖) overlayer systems [13]. Both photoemission [9] and inverse photoemission [10][11][12] have detected flat bands perpendicular to the atom rows and a Fermi level crossing in single domain samples at ഠ0.6 GX parallel to the atom rows. Consequently, the experimental evidence suggests that the 4 3 1 system may contain the smallest known metallic wires in existence. The possibility of integrating these naturally occurring wires into practical electronic devices remains a dream. However, recent developments in lithography [14] have demonstrated that it should be possible to continue to reduce the size of electronic devices down to the atomic or molecular limit where the wires could be used as atomic scale interconnects.In the course of our study of the 4 3 1 system [10-12], we discovered an image-induced surface state located 0.67 6 0.15 eV below the vacuum level at theḠ point. Image-induced surface states are spatially confined by both the surface barrier and the long-range image potential [15][16][17]. What makes these states particularly interesting is that the image potential is associated with electrons in an array of ordered metallic wires that are only a few atoms wide. In fact, the surface structure resembles an atomic scale diffraction grating with a translational symmetry that is quite unlike that of the low index metal surfaces where image states have been extensively studied [18]. Consequently, the form of the surface potential may also be different, and...

Free-electron response in reflectance anisotropy spectra

“…Indeed, for Si͑111͒ : In-͑4 ϫ 1͒, it is already known that there is an anisotropy in the effective mass of the electrons and hence the plasma frequency p in the metallic band. 52 This more sophisticated model could not be applied because the total number of parameters becomes too large to be useful ͑in the absence of additional data allowing some of these to be fixed͒, and the spectral range is already too small for definitive fits even with the simpler model. In the case of the tin islands, where the free electron contribution was shown to be dominant, fits allowing for an anisotropic p produced a p,y / p,x ratio that varied between 0.97 and 1.03, showing that the anisotropy in the scattering rate is indeed more dominant ͑␥ y / ␥ x between 1.1 and 1.5͒ as was suggested in the Introduction.…”

Structure of Si(111)-In Nanowires Determined from the Midinfrared Optical Response

“…Results from many different experiments, as well as ab initio band structure calculations, agree that the structure is metallic, with the In atoms forming two parallel zigzag chains, which are separated by zigzag Si chains that resemble the -bonded chains of Sið111Þ-ð2 Â 1Þ [3][4][5][6][7][8][9][10][11][12][13][14]. The structure has three quasi-1D surface state bands, which disperse strongly and cross the Fermi level along the chain direction, and show only a weak dispersion perpendicular to the chain.…”

Structure determination of the indium-inducedSi(111)−(4×1)reconstruction by surface x-ray diffraction

“…Additionally to this interesting electronic property the surface exhibits an image state that also showed quasi-1d behavior in its strongly anisotropic dispersion: Along a certain direction the dispersion is very well described by a free electron parabola whereas in the perpendicular direction the dispersion falls below the free electron parabola. 6 Scanning tunneling microscopy (STM) investigations of the Si(111)-(4×1)-In reconstruction 1,7-11 resolved zig-zag chains running in the 110 directions in the filled-state images and linear chains in the empty-state images. Tunneling data was acquired at bias voltages down to 0.04 V consistent with metallic behavior in agreement with scanning tunneling spectroscopy results.…”